A thorough study of interrelationship in fuzzy implication axioms

Yun Shi; Bart Van Gasse; Da Ruan; Etienne Kerre; Özgür Kabak

A thorough study of interrelationship in fuzzy implication axioms

Yun Shi, Bart Van Gasse, Da Ruan, Etienne Kerre, Özgür Kabak

Research output › peer-review

Abstract

A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which eight axioms are most important. Different authors have investigated the dependence and independence of the eight axioms but the investigation is yet not complete. We study a complete interrelationship of all the eight axioms, and give for each independence case a counter-example.

Original language	English
Title of host publication	Intelligent Decision Making Systems
Place of Publication	Singapore, Singapore
Pages	52-57
Volume	1
State	Published - Nov 2009
Event	The 4th Int. ISKE Conference on Intelligent Decision Making Systems - Hasselt Duration: 27 Nov 2009 → 28 Nov 2009

Publication series

Name	Computer Engineering and Information Science
Number	2

Conference

Conference	The 4th Int. ISKE Conference on Intelligent Decision Making Systems
Country/Territory	Belgium
City	Hasselt
Period	2009-11-27 → 2009-11-28

Cite this

@inproceedings{2d8d4f0106dc4e658370ff9e65cc6098,

title = "A thorough study of interrelationship in fuzzy implication axioms",

abstract = "A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which eight axioms are most important. Different authors have investigated the dependence and independence of the eight axioms but the investigation is yet not complete. We study a complete interrelationship of all the eight axioms, and give for each independence case a counter-example.",

keywords = "fuzzy implications, fuzzy implication axioms, approximate reasoning",

author = "Yun Shi and {Van Gasse}, Bart and Da Ruan and Etienne Kerre and {\"O}zg{\"u}r Kabak",

note = "Score = 3; The 4th Int. ISKE Conference on Intelligent Decision Making Systems ; Conference date: 27-11-2009 Through 28-11-2009",

year = "2009",

month = nov,

language = "English",

isbn = "978-981-4295-05-5",

volume = "1",

series = "Computer Engineering and Information Science",

number = "2",

pages = "52--57",

booktitle = "Intelligent Decision Making Systems",

}

TY - GEN

T1 - A thorough study of interrelationship in fuzzy implication axioms

AU - Shi, Yun

AU - Van Gasse, Bart

AU - Ruan, Da

AU - Kerre, Etienne

A2 - Kabak, Özgür

N1 - Score = 3

PY - 2009/11

Y1 - 2009/11

N2 - A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which eight axioms are most important. Different authors have investigated the dependence and independence of the eight axioms but the investigation is yet not complete. We study a complete interrelationship of all the eight axioms, and give for each independence case a counter-example.

AB - A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which eight axioms are most important. Different authors have investigated the dependence and independence of the eight axioms but the investigation is yet not complete. We study a complete interrelationship of all the eight axioms, and give for each independence case a counter-example.

KW - fuzzy implications

KW - fuzzy implication axioms

KW - approximate reasoning

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_101594

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_101594_2

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_101594_3

UR - http://knowledgecentre.sckcen.be/so2/bibref/6303

M3 - In-proceedings paper

SN - 978-981-4295-05-5

VL - 1

T3 - Computer Engineering and Information Science

SP - 52

EP - 57

BT - Intelligent Decision Making Systems

CY - Singapore, Singapore

T2 - The 4th Int. ISKE Conference on Intelligent Decision Making Systems

Y2 - 27 November 2009 through 28 November 2009

ER -